--- title: "Using a delay-adjusted case fatality ratio to estimate under-reporting" description: "Using a corrected case fatality ratio, we calculate estimates of the level of under-reporting for any country with greater than ten deaths" status: real-time-report rmarkdown_html_fragment: true update: 2020-08-04 authors: - id: tim_russell corresponding: true - id: joel_hellewell equal: 1 - id: sam_abbott equal: 1 - id: nick_golding - id: hamish_gibbs - id: chris_jarvis - id: kevin_vanzandvoort - id: ncov-group - id: stefan_flasche - id: roz_eggo - id: john_edmunds - id: adam_kucharski ---

Aim

To estimate the percentage of symptomatic COVID-19 cases reported in different countries using case fatality ratio estimates based on data from the ECDC, correcting for delays between confirmation-and-death.

Data availability

The under-reporting estimates for all countries can be downloaded as a single .csv file here.

Similarly, the prevalence estimates can be downloaded as a single .csv file here.

How to cite this work

If you wish to cite this work, please do cite the associated preprint [1]).

Methods Summary

The associated preprint[1], specifically the corresponding supplementary material contains a full description of the methods and limitations used to arrive at the estimates presented here.

Current estimates of under-reporting, prevalence and adjusted case curves along with reported cases

Temporal variation

Figure 1: Temporal variation in reporting rate. We calculate the percentage of symptomatic cases reported on each day a country has had more than ten deaths. We then fit a Gaussian Process (GP) to these data (see Temporal variation model fitting section for details), highlighting the temporal trend of each countries reporting rate. The red shaded region is the 95% CrI of fitted GP.

Prevalence estimates

Country Prevalence median (95% CrI) Total reported cases New reported cases (tallied over last 10 days) Population
Afghanistan 0.11% (0.05% - 0.26%) 22,890 9,231 38,928,341
Albania 0.023% (0.013% - 0.075%) 1,385 286 2,877,800
Algeria 0.027% (0.013% - 0.066%) 10,589 1,455 43,851,043
Andorra 0.69% (0.21% - 2.3%) 852 88 77,265
Argentina 0.12% (0.059% - 0.26%) 27,360 11,954 45,195,777
Armenia 0.77% (0.39% - 1.7%) 14,669 5,993 2,963,234
Australia 0.00097% (0.00057% - 0.0022%) 7,285 112 25,499,881
Austria 0.016% (0.0058% - 0.046%) 16,964 370 9,006,400
Azerbaijan 0.099% (0.051% - 0.23%) 8,882 3,893 10,139,175
Bahamas 0.00085% (0.00033% - 0.0049%) 103 1 393,248
Bahrain 0.82% (0.52% - 1.5%) 17,269 6,820 1,701,583
Bangladesh 0.055% (0.028% - 0.12%) 78,052 35,208 164,689,383
Belarus 0.24% (0.15% - 0.45%) 51,816 11,052 9,449,321
Belgium 0.086% (0.044% - 0.2%) 59,711 1,650 11,589,616
Bolivia 0.36% (0.19% - 0.77%) 16,165 7,434 11,673,029
Bosnia and Herzegovina 0.04% (0.015% - 0.16%) 2,831 346 3,280,815
Brazil 1.1% (0.61% - 2.3%) 802,828 337,662 212,559,409
Bulgaria 0.085% (0.04% - 0.22%) 3,086 587 6,948,445
Burkina Faso 0.00077% (0.00029% - 0.0029%) 892 45 20,903,278
Cameroon 0.026% (0.016% - 0.053%) 8,681 3,245 26,545,864
Canada 0.2% (0.11% - 0.42%) 97,519 8,112 37,742,157
Chad 0.0019% (0.00075% - 0.0083%) 848 89 16,425,859
Chile 0.71% (0.43% - 3.8%) 154,092 63,454 19,116,209
China 2.9e-05% (1e-05% - 0.00015%) 84,216 93 1,439,323,774
Colombia 0.19% (0.1% - 0.41%) 43,682 16,994 50,882,884
Congo 0.013% (0.0048% - 0.041%) 745 158 5,518,092
Costa Rica 0.024% (0.013% - 0.064%) 1,538 516 5,094,114
Côte d’Ivoire 0.014% (0.0081% - 0.029%) 4,404 1,654 26,378,275
Croatia 0.00089% (3e-04% - 0.0035%) 2,249 4 4,105,268
Cuba 0.0048% (0.0025% - 0.014%) 2,219 214 11,326,616
Cyprus 0.0068% (0.0037% - 0.021%) 975 34 1,207,361
Czechia 0.021% (0.0088% - 0.055%) 9,886 690 10,708,982
Democratic Republic of the Congo 0.005% (0.0024% - 0.015%) 4,514 1,681 89,561,404
Denmark 0.026% (0.012% - 0.069%) 12,035 442 5,792,203
Djibouti 0.33% (0.2% - 0.73%) 4,398 1,484 988,002
Dominican Republic 0.1% (0.059% - 0.22%) 21,437 4,906 10,847,904
Ecuador 0.25% (0.13% - 0.54%) 44,440 5,869 17,643,060
Egypt 0.091% (0.048% - 0.19%) 39,726 17,644 102,334,403
El Salvador 0.067% (0.031% - 0.16%) 3,481 1,203 6,486,201
Equatorial Guinea 0.042% (0.024% - 0.095%) 1,306 263 1,402,985
Estonia 0.041% (0.015% - 0.11%) 1,965 106 1,326,539
Ethiopia 0.0072% (0.0031% - 0.018%) 2,670 1,702 114,963,583
Finland 0.014% (0.0068% - 0.04%) 7,064 288 5,540,718
France 0.052% (0.028% - 0.11%) 155,561 5,893 65,273,512
Gabon 0.08% (0.05% - 0.16%) 3,463 850 2,225,728
Georgia 0.0054% (0.0028% - 0.016%) 831 85 3,989,175
Germany 0.03% (0.015% - 0.064%) 185,674 4,478 83,783,945
Ghana 0.018% (0.011% - 0.033%) 10,358 2,742 31,072,945
Greece 0.015% (0.0063% - 0.043%) 3,088 179 10,423,056
Guatemala 0.28% (0.13% - 0.66%) 8,561 3,954 17,915,567
Guinea 0.011% (0.0071% - 0.022%) 4,372 716 13,132,792
Guyana 0.0038% (0.0013% - 0.021%) 158 8 786,559
Haiti 0.049% (0.027% - 0.12%) 3,941 2,357 11,402,533
Honduras 0.19% (0.085% - 0.47%) 7,669 2,783 9,904,608
Hungary 0.029% (0.013% - 0.072%) 4,039 198 9,660,350
Iceland 0.0014% (0.00076% - 0.004%) 1,807 2 341,250
India 0.057% (0.031% - 0.12%) 297,535 123,772 1,380,004,385
Indonesia 0.033% (0.017% - 0.068%) 35,295 10,079 273,523,621
Iran 0.18% (0.094% - 0.36%) 180,176 33,508 83,992,953
Iraq 0.21% (0.11% - 0.45%) 16,675 10,802 40,222,503
Ireland 0.08% (0.034% - 0.22%) 25,238 362 4,937,796
Isle of Man 0% (0% - 0%) 336 0 85,032
Israel 0.049% (0.026% - 0.11%) 18,701 1,714 8,655,541
Italy 0.11% (0.057% - 0.22%) 236,142 3,894 60,461,828
Japan 0.0026% (0.0012% - 0.0065%) 17,332 528 126,476,458
Kazakhstan 0.038% (0.024% - 0.074%) 13,872 3,490 18,776,707
Kenya 0.011% (0.0048% - 0.029%) 3,215 1,470 53,771,300
Kosovo 0.042% (0.02% - 0.12%) 1,326 278 1,810,366
Kuwait 0.45% (0.28% - 0.82%) 34,432 9,248 4,270,563
Kyrgyzstan 0.016% (0.0088% - 0.041%) 2,166 444 6,524,191
Latvia 0.0068% (0.0025% - 0.023%) 1,094 30 1,886,202
Lebanon 0.0087% (0.0044% - 0.027%) 1,402 230 6,825,442
Liberia 0.021% (0.0059% - 0.081%) 410 137 5,057,677
Lithuania 0.023% (0.0096% - 0.076%) 1,752 90 2,722,291
Luxembourg 0.023% (0.01% - 0.061%) 4,052 40 625,976
Malaysia 0.0041% (0.0026% - 0.0082%) 8,369 637 32,365,998
Mali 0.023% (0.01% - 0.054%) 1,722 496 20,250,834
Mauritania 0.18% (0.072% - 0.48%) 1,162 739 4,649,660
Mauritius 5e-04% (2e-04% - 0.003%) 337 2 1,271,767
Mexico 0.94% (0.51% - 1.9%) 133,974 49,347 128,932,753
Moldova 0.44% (0.22% - 0.94%) 10,727 2,831 4,033,963
Morocco 0.0046% (0.0029% - 0.0099%) 8,537 823 36,910,558
Netherlands 0.075% (0.036% - 0.17%) 48,251 2,125 17,134,873
New Zealand 0% (0% - 0%) 1,154 0 4,822,233
Nicaragua 0.031% (0.014% - 0.18%) 1,464 705 6,624,554
Niger 0.00049% (0.00013% - 0.002%) 974 19 24,206,636
Nigeria 0.01% (0.0051% - 0.023%) 14,554 5,252 206,139,587
North Macedonia 0.63% (0.3% - 1.4%) 3,542 1,412 2,083,380
Norway 0.0092% (0.0044% - 0.039%) 8,594 183 5,421,242
Oman 0.41% (0.26% - 0.74%) 19,954 10,134 5,106,622
Pakistan 0.12% (0.063% - 0.24%) 125,933 59,476 220,892,331
Panama 0.76% (0.38% - 1.7%) 18,586 6,055 4,314,768
Paraguay 0.0094% (0.0057% - 0.02%) 1,230 313 7,132,530
Peru 0.93% (0.5% - 1.9%) 214,788 66,503 32,971,846
Philippines 0.018% (0.0099% - 0.038%) 24,175 7,541 109,581,085
Poland 0.067% (0.032% - 0.16%) 28,201 5,046 37,846,605
Portugal 0.19% (0.093% - 0.43%) 35,910 3,964 10,196,707
Puerto Rico 0.13% (0.077% - 0.28%) 5,352 1,705 2,860,840
Qatar 1.9% (1% - 10%) 75,071 22,164 2,881,060
Romania 0.085% (0.043% - 0.2%) 21,182 2,200 19,237,682
Russia 0.25% (0.15% - 0.49%) 502,436 114,813 145,934,460
San Marino 0.14% (0.077% - 0.59%) 691 20 33,938
Sao Tome and Principe 0.2% (0.1% - 0.62%) 639 176 219,161
Saudi Arabia 0.49% (0.25% - 1%) 116,021 34,255 34,813,867
Senegal 0.018% (0.01% - 0.041%) 4,759 1,330 16,743,930
Serbia 0.018% (0.011% - 0.042%) 12,102 748 8,737,370
Sierra Leone 0.01% (0.0044% - 0.032%) 1,085 256 7,976,985
Singapore 0.21% (0.12% - 0.62%) 39,387 5,527 5,850,343
Sint Maarten 0% (0% - 0%) 77 0 42,882
Slovakia 0.001% (5e-04% - 0.003%) 1,541 21 5,459,643
Slovenia 0.0076% (0.0025% - 0.023%) 1,488 15 2,078,932
Somalia 0.013% (0.006% - 0.037%) 2,513 685 15,893,219
South Africa 0.27% (0.15% - 0.56%) 58,568 29,328 59,308,690
South Korea 0.0029% (0.0014% - 0.0083%) 12,003 562 51,269,183
South Sudan 0.014% (0.0071% - 0.037%) 1,604 610 11,193,729
Spain 0.022% (0.012% - 0.097%) 242,707 3,479 46,754,783
Sri Lanka 0.0032% (0.0019% - 0.0069%) 1,877 319 21,413,250
Sudan 0.059% (0.027% - 0.14%) 6,730 2,209 43,849,269
Sweden 0.72% (0.38% - 1.5%) 48,288 11,812 10,099,270
Switzerland 0.016% (0.0074% - 0.039%) 30,961 216 8,654,618
Tajikistan 0.027% (0.017% - 0.049%) 4,834 1,271 9,537,642
Thailand 0.00018% (9.1e-05% - 0.00049%) 3,125 49 69,799,978
Togo 0.0028% (0.0015% - 0.0082%) 524 96 8,278,737
Tunisia 0.00052% (0.00018% - 0.0023%) 1,087 16 11,818,618
Turkey 0.035% (0.019% - 0.072%) 174,023 11,903 84,339,067
Ukraine 0.064% (0.031% - 0.15%) 29,070 5,866 43,733,759
United Arab Emirates 0.16% (0.1% - 0.3%) 40,986 7,816 9,890,400
United Kingdom 0.45% (0.24% - 0.92%) 291,409 20,187 67,886,004
United Republic of Tanzania 0% (0% - 0%) 509 0 59,734,213
United States of America 0.44% (0.24% - 0.89%) 2,023,347 276,260 331,002,647
Uruguay 0.0033% (0.0012% - 0.011%) 847 31 3,473,727
Uzbekistan 0.0081% (0.0051% - 0.016%) 4,819 1,306 33,469,199
Venezuela 0.011% (0.0066% - 0.023%) 2,814 1,445 28,435,943
Yemen 0.049% (0.022% - 0.11%) 591 304 29,825,968

Table 1: Estimates for the prevalence of COVID-19 in each country with greater than 10 deaths. We use the under-reporting estimates to adjust the reported case curves and tally these up over the last ten days as a proxy for prevalence. See Detailed Methods for more details.

Adjusted symptomatic case estimates

Figure 2: Estimated number of new symptomatic cases, calculated using our temporal under-reporting estimates. We adjust the reported case numbers each day - for each country with an under-reporting estimate - using our temporal under-reporting estimates to arrive at an estimate of the true number of symptomatic cases each day. The shaded blue region represents the 95% CrI, calcuated directly using the 95% CrI of the temporal under-reporting estimate.

Reported cases

Figure 3: Reported number of cases each day, pulled from the ECDC and plotted against time for comparison with our estimated true numbers of symptomatic cases each day, adjusted using our under-reporting estimates.

Current under-reporting estimates

Country Percentage of symptomatic cases reported (95% CI) Total cases Total deaths
Afghanistan 51% (37%-67%) 36,747 1,288
Albania 33% (22%-48%) 5,620 172
Algeria 66% (51%-85%) 31,972 1,239
Andorra 53% (21%-98%) 937 52
Angola 24% (16%-35%) 1,164 54
Argentina 59% (50%-68%) 201,906 3,667
Armenia 70% (58%-86%) 39,102 762
Australia 65% (41%-96%) 18,318 221
Austria 94% (70%-100%) 21,341 718
Azerbaijan 87% (73%-99%) 32,684 468
Bahamas 75% (38%-100%) 679 14
Bahrain 99% (95%-100%) 41,835 150
Bangladesh 99% (94%-100%) 242,102 3,184
Belarus 33% (21%-49%) 68,166 571
Belgium 95% (83%-100%) 70,221 9,850
Benin 73% (47%-99%) 1,805 36
Bolivia 22% (19%-26%) 81,846 3,228
Bosnia and Herzegovina 41% (29%-56%) 12,296 347
Brazil 57% (50%-63%) 2,750,318 94,665
Bulgaria 51% (38%-67%) 11,955 388
Burkina Faso 83% (42%-100%) 1,153 54
Cameroon 99% (90%-100%) 17,255 387
Canada 92% (76%-100%) 117,017 8,947
Cape Verde 91% (69%-100%) 2,583 25
Central African Republic 95% (70%-100%) 4,614 59
Chad 79% (23%-100%) 936 75
Chile 76% (34%-100%) 361,493 9,707
China 99% (86%-100%) 88,099 4,672
Colombia 32% (29%-36%) 327,850 11,017
Congo 92% (70%-100%) 3,546 58
Costa Rica 93% (71%-100%) 19,402 171
Cote dIvoire 99% (93%-100%) 16,220 102
Croatia 64% (34%-97%) 5,296 153
Cuba 89% (50%-100%) 2,670 87
Cyprus 85% (50%-100%) 1,155 19
Czechia 96% (78%-100%) 17,008 386
Democratic Republic of the Congo 85% (50%-100%) 9,132 214
Denmark 90% (66%-100%) 13,996 616
Djibouti 92% (67%-100%) 5,240 59
Dominican Republic 97% (88%-100%) 73,117 1,183
Ecuador 40% (33%-48%) 87,041 5,767
Egypt 28% (24%-34%) 94,640 4,888
El Salvador 53% (41%-70%) 17,843 486
Equatorial Guinea 8.1% (3.3%-15%) 4,821 83
Estonia 64% (30%-99%) 2,080 69
Eswatini 62% (42%-89%) 2,838 45
Ethiopia 63% (51%-80%) 19,289 336
Finland 87% (44%-100%) 7,466 329
France 83% (62%-95%) 191,295 30,294
Gabon 98% (90%-100%) 7,646 51
Georgia 84% (51%-100%) 1,182 17
Germany 99% (95%-100%) 211,281 9,156
Ghana 99% (96%-100%) 37,812 191
Greece 62% (31%-99%) 4,737 209
Guatemala 33% (27%-40%) 51,542 2,013
Guinea 97% (87%-100%) 7,364 46
Guinea Bissau 76% (47%-100%) 1,981 27
Guyana 40% (19%-77%) 474 21
Haiti 60% (31%-96%) 7,511 166
Honduras 29% (23%-34%) 43,794 1,384
Hungary 58% (26%-98%) 4,544 597
Iceland 87% (48%-100%) 1,915 10
India 81% (73%-98%) 1,855,745 38,938
Indonesia 39% (33%-46%) 113,134 5,302
Iran 16% (14%-18%) 312,035 17,405
Iraq 48% (41%-55%) 131,886 4,934
Ireland 38% (22%-67%) 26,208 1,763
Israel 99% (94%-100%) 74,903 546
Italy 41% (32%-52%) 248,229 35,166
Jamaica 79% (36%-100%) 905 12
Japan 100% (98%-100%) 39,858 1,016
Jordan 82% (45%-100%) 1,218 22
Kazakhstan 87% (69%-100%) 93,820 1,058
Kenya 62% (47%-79%) 22,597 382
Kosovo 20% (12%-29%) 9,049 256
Kuwait 99% (93%-100%) 68,299 461
Kyrgyzstan 95% (26%-100%) 37,541 1,427
Latvia 47% (24%-83%) 1,246 32
Lebanon 87% (59%-100%) 5,062 65
Liberia 45% (12%-100%) 1,214 78
Libya 45% (33%-64%) 4,063 93
Lithuania 55% (29%-96%) 2,120 80
Luxembourg 95% (79%-100%) 6,864 118
Madagascar 93% (77%-100%) 11,660 118
Malawi 29% (20%-40%) 4,273 123
Malaysia 91% (45%-100%) 9,001 125
Maldives 93% (73%-100%) 4,293 18
Mali 78% (41%-100%) 2,543 124
Mauritania 98% (81%-100%) 6,323 157
Mexico 15% (13%-17%) 443,813 48,012
Moldova 51% (41%-63%) 25,482 800
Montenegro 71% (49%-97%) 3,301 52
Morocco 43% (32%-59%) 26,196 401
Mozambique 88% (61%-100%) 1,973 14
Nepal 98% (89%-100%) 20,750 57
Netherlands 96% (82%-100%) 55,415 6,140
New Zealand 59% (25%-99%) 1,217 22
Nicaragua 76% (38%-100%) 3,672 116
Niger 63% (21%-100%) 1,152 69
Nigeria 93% (82%-100%) 44,129 896
North Macedonia 37% (29%-47%) 11,140 500
Norway 84% (46%-100%) 9,268 256
Oman 99% (96%-100%) 79,159 421
Pakistan 96% (88%-100%) 280,461 5,999
Palestine 99% (93%-100%) 16,024 87
Panama 52% (43%-63%) 68,456 1,497
Paraguay 94% (75%-100%) 5,724 55
Peru 84% (31%-100%) 433,100 19,811
Philippines 100% (100%-100%) 106,330 2,104
Poland 65% (50%-82%) 47,469 1,732
Portugal 98% (83%-100%) 51,569 1,738
Puerto Rico 98% (82%-100%) 18,791 230
Qatar 85% (40%-100%) 111,322 177
Romania 40% (33%-48%) 54,009 2,432
Russia 62% (55%-69%) 856,264 14,207
Sao Tome and Principe 86% (52%-100%) 874 15
Saudi Arabia 75% (61%-89%) 280,093 2,949
Senegal 55% (40%-75%) 10,386 211
Serbia 74% (56%-93%) 26,451 598
Sierra Leone 83% (40%-100%) 1,848 67
Singapore 95% (73%-100%) 53,051 27
Sint Maarten 24% (6.7%-81%) 150 16
Slovakia 90% (67%-100%) 2,354 29
Slovenia 73% (39%-100%) 2,181 117
Somalia 93% (61%-100%) 3,220 93
South Africa 65% (57%-73%) 516,862 8,539
South Korea 94% (69%-100%) 14,423 301
South Sudan 74% (47%-99%) 2,429 46
Sri Lanka 96% (82%-100%) 2,828 11
Sudan 21% (14%-33%) 11,738 752
Suriname 82% (55%-100%) 1,893 27
Sweden 71% (54%-91%) 81,012 5,744
Switzerland 96% (81%-100%) 35,527 1,706
Syria 17% (11%-28%) 847 46
Tajikistan 96% (67%-100%) 7,538 61
Thailand 83% (51%-100%) 3,321 58
Togo 82% (46%-100%) 976 19
Tunisia 84% (45%-100%) 1,565 51
Turkey 87% (71%-99%) 233,851 5,747
Ukraine 67% (55%-80%) 73,158 1,738
United Arab Emirates 98% (83%-100%) 61,163 351
United Kingdom 15% (13%-18%) 305,623 46,210
United States of America 84% (67%-100%) 4,713,562 155,403
Uruguay 44% (26%-73%) 1,291 36
Uzbekistan 98% (91%-100%) 26,550 161
Venezuela 97% (87%-100%) 20,206 174
Yemen 6.6% (3.8%-11%) 1,738 499
Zambia 39% (22%-68%) 6,580 171
Zimbabwe 37% (26%-50%) 4,075 80

Table 2: Estimates for the proportion of symptomatic cases reported in different countries using cCFR estimates based on case and death timeseries data from the ECDC. Total cases and deaths in each country is also shown. Confidence intervals calculated using an exact binomial test with 95% significance.

Adjusting for outcome delay in CFR estimates

During an outbreak, the naive CFR (nCFR), i.e. the ratio of reported deaths date to reported cases to date, will underestimate the true CFR because the outcome (recovery or death) is not known for all cases [6]. We can therefore estimate the true denominator for the CFR (i.e. the number of cases with known outcomes) by accounting for the delay from confirmation-to-death [2].

We assumed the delay from confirmation-to-death followed the same distribution as estimated hospitalisation-to-death, based on data from the COVID-19 outbreak in Wuhan, China, between the 17th December 2019 and the 22th January 2020, accounting right-censoring in the data as a result of as-yet-unknown disease outcomes (Figure 1, panels A and B in [8]). The distribution used is a Lognormal fit, has a mean delay of 13 days and a standard deviation of 12.7 days [8].

To correct the CFR, we use the case and death incidence data to estimate the proportion of cases with known outcomes [2,7]:

\[ u_{t} = \frac{ \sum_{j = 0}^{t} c_{t-j} f_j}{c_t}, \]

where \(u_t\) represents the underestimation of the proportion of cases with known outcomes [2,6,7] and is used to scale the value of the cumulative number of cases in the denominator in the calculation of the cCFR, \(c_{t}\) is the daily case incidence at time, \(t\) and \(f_t\) is the proportion of cases with delay of \(t\) between confirmation and death.

Approximating the proportion of symptomatic cases reported

At this stage, raw estimates of the CFR of COVID-19 correcting for delay to outcome, but not under-reporting, have been calculated. These estimates range between 1% and 1.5% [2–4]. We assume a CFR of 1.4% (95% CrI: 1.2-1.7%), taken from a recent large study [4], as a baseline CFR. We use it to approximate the potential level of under-reporting in each country. Specifically, we perform the calculation \(\frac{1.4\%}{\text{cCFR}}\) of each country to estimate an approximate fraction of cases reported.

Temporal variation model fitting

We estimate the level of under-reporting on every day for each country that has had more than ten deaths. We then fit a Gaussian Process (GP) model using the library greta and greta.gp. The parameters we fit and their priors are the following: \[ \begin{aligned} &\sigma \sim \text{Log Normal(-1, 1)}: \quad &\text{Variance of the reporting kernel} \\ &\text{L} \sim \text{Log Normal(4, 0.5)}: \quad &\text{Lengthscale of the reporting kernel} \\ &\sigma_{\text{obs}} \sim \text{Truncated Normal(0, 0.5)}, \quad &\text{Variance of the obseration kernel, truncated at 0} \end{aligned} \] The kernel is split into two components: the reporting kernel \(R\), and the observation kernel \(O\). The reporting component has a standard squared-exponential form. For the observation component, we use an i.i.d. noise kernel to acccount for observation overdispersion, which can smooth out overly clumped death time-series. This is important as some countries have been known to report an unusually large number of deaths on a single day, due to past under-reporting.

In the sampling and fitting process, we calculate the expected number of deaths at each time-point, given the baseline CFR. We then use a Poisson likelihood, where the expected number of deaths is the rate of the Poisson likelihood, given the observed number of deaths

Approximating prevalence

We use the adjusted case curves, adjusted for under-reporting and for asymptomatic infections as a proxy for prevalence. Specifically, we tally up the adjusted new cases each day over the last ten days and calculate what percentage of the population in question this total equates to. This serves as a crude prevalence estimate. We assume ten days of infectiousness as taken from the mean of the total infectious period [9].

Adjusting case counts for under-reporting

We adjust the reported number of cases each day, pulled from the ECDC. Specifically, we divide the case numbers of each day by our “proportion of cases reported” estimates that we calculate each day for each country.*

Limitations

Implicit in assuming that the under-reporting is \(\frac{1.4\%}{\text{cCFR}}\) for a given country is that the deviation away from the assumed 1.4% CFR is entirely down to under-reporting. In reality, burden on healthcare system is a likely contributing factor to higher than 1.4% CFR estimates, along with many other country specific factors.

The following is a list of the other prominent assumptions made in our analysis:

Code and data availability

The code is publically available at https://github.com/thimotei/CFR_calculation. The data required for this analysis is a time-series for both cases and deaths, along with the corresponding delay distribution. We scrape this data from ECDC, using the NCoVUtils package [10].

The under-reporting estimates for all countries can be downloaded as a single .csv file here.

Similarly, global prevalence estimates can be downloaded as a single .csv file here

Acknowledgements

The authors, on behalf of the Centre for the Mathematical Modelling of Infectious Diseases (CMMID) COVID-19 working group, wish to thank DSTL for providing the High Performance Computing facilities and associated expertise that has enabled these models to be prepared, run and processed and in an appropriately-rapid and highly efficient manner.

References

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